Problem: Which of these numbers is prime? ${25,\ 27,\ 42,\ 53,\ 65}$
Solution: A prime number has exactly two factors: 1 and itself. The factors of 25 are 1, 5, and 25. The factors of 27 are 1, 3, 9, and 27. The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42. The factors of 53 are 1 and 53. The factors of 65 are 1, 5, 13, and 65. Thus, 53 is a prime number.